The Constitution specifically delegates to the Federal Government the power to deal with insurrection. Article VI makes it quite plain that secession is an act of insurrection.
Only elements of South Carolina fired on federal troops who had refused to leave. That was an error made in haste.
An insurrection would have been to overthrow the federal government, such as if D.C. had been invaded and Lincoln with other high officials arrested as a new extra-Constitutional regime was installed, not just leaving the Union behind.